Well-posedness for Hardy-Hénon parabolic equations with fractional Brownian noise

Abstract

We study the Hardy-Hénon parabolic equations on ${\mathbb{R}}^N$ ($N=2,3$) under the effect of an additive fractional Brownian noise with Hurst parameter $H>\max \left(1/2,N/4\right).$ We show local existence and uniqueness of a mid $L^q$-solution under suitable assumptions on $q$.